Friezes, Strings and Cluster Variables
Commutative Algebra
2011-03-15 v2
Abstract
To any walk in a quiver, we associate a Laurent polynomial. When the walk is the string of a string module over a 2-Calabi-Yau tilted algebra, we prove that this Laurent polynomial coincides with the corresponding cluster character of the string module, up to an explicit normalising monomial factor.
Cite
@article{arxiv.1009.3341,
title = {Friezes, Strings and Cluster Variables},
author = {Ibrahim Assem and Grégoire Dupont and Ralf Schiffler and David Smith},
journal= {arXiv preprint arXiv:1009.3341},
year = {2011}
}
Comments
Some minor typos were fixed and some sections were shortened; to appear in Glasgow Mathematical Journal (2011) 32 pages